1. Field of the Invention
This invention relates to a digital image recording apparatus and a digital image recording method. More particularly, this invention relates to an apparatus and method for visually completely restoring on a recording medium image information components at frequencies not higher than the Nyquist rate.
2. Description of the Related Art
Image recording apparatus for recording a digital image in an actual size or to an enlarged or reduced scale, such as laser printers, thermal printers and the like, are known. In such an image recording apparatus, a digital image signal obtained by sampling an analog image signal is subjected to a predetermined image processing, for instance, to an interpolation processing, in the case where the image is to be enlarged and then reproduced on an image recording medium.
Recording by the image recording apparatus is equivalent to restoring a digital image signal as an analog image signal. As a theorem for restoring such a digital signal, a sampling theorem is known. The sampling theorem defines a condition on sampling intervals for completely restoring the digital signal as an analog signal. For example, in a one-dimensional sampling theorem, it has been proven that when an analog signal is sampled at a sampling frequency N (sampling intervals of 1/N), the signal components at frequencies not higher than N/2 included in the analog signal can be completely restored. The frequency of N/2 is generally referred to as "the Nyquist rate". Further is known that when a digital signal including therein frequency components higher than the Nyquist rate is restored to an analog signal, error occurs due to folding of a high frequency side part toward a low frequency side (aliasing error), thereby causing the shape of the restored analog signal to be greatly deformed. As for an image signal, a two-dimensional sampling theorem shows that the signal components at frequencies not higher than the Nyquist rate can be completely restored and that when a digital signal includes frequency components higher than the Nyquist rate, the digital signal cannot be completely restored as and analog signal.
Accordingly it seems that signal components at a frequency not higher than the Nyquist rate can be visually completely restored by the image recording apparatus if sampling or recording of an image is carried out on the basis of the sampling theorem. However in conventional image processing systems, signal components at frequencies not higher than the Nyquist rate actually cannot be visually completely restored in conformity with the theorem.
This is because of the following fact. That is, since the sampling theorem assumes that the original waveform can be restored by convoluting a sinc function ((sin x)/x) in sampled values, the response to recording of the recording medium must be a sinc function in order to record an image according to the sampling theorem. In other words, the recording medium must be such that a picture element is recorded on the recording medium at a density corresponding to a value which is obtained by convoluting the sinc function in a value of a given digital signal component. However since the sinc function can take on a negative value whereas the response of recording on a recording medium cannot be negative, the sinc function cannot truly be convoluted.
That is, it is actually impossible to visually completely restore the signal components at frequencies not higher than the Nyquist rate on a recording medium. However since the sampling theorem has been widely known and because various systems other than recording systems are designed according to the sampling theorem, the image recording apparatus has been expected, as if natural, to be able to visually completely restore the signal components of frequencies not higher than the Nyquist rate according to the sampling theorem.